Finite Group Databasebeta

← #15749599

Subgroups — #15749599

Order 3328.

286 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13115846C211yesmaximal, characteristic
2#13112704C211yesmaximal, characteristic
3C13×#1314C211yesmaximal, characteristic
4C2×#88178—21no—
5C22×Dic52C411yescharacteristic, complemented
6C2×C13×C22⋊C8C2211yescharacteristic
7#11718873—21no—
8C2×#88056—21no—
9C13×C22⋊C16—21no—
10#11718143C411yescharacteristic, complemented
11C23×C4×C13D411yescharacteristic
12C22×Dic26—21no—
13C22×C8×C13C2×C411yescharacteristic
14C22×C8×C13D411yescharacteristic
15C2×C22⋊Dic13—41no—
16C2×C22⋊Dic13—41no—
17C2×C4⋊Dic13—21no—
18C2×C4⋊Dic13—41no—
19#88178—42no—
20#88178—42no—
21C2×#6101—41no—
22C2×Dic52—41no—
23C2×Dic52—42no—
24C2×C13×C16—41no—
25C13×C22⋊C8—41no—
26#88071—22no—
27#88056—42no—
28#7078—131nomaximal, Sylow
29C24×C13D811yescharacteristic
30C22×C4×C13—21no—
31C22×C4×C13—21no—
32C22×C4×C13—41no—
33C22×C4×C13—41no—
34C22×C4×C13C22⋊C411yescharacteristic
35C22×C4×C13SD1611yescharacteristic
36C22×Dic13—41no—
37C22×Dic13—41no—
38C22×Dic13—42no—
39C2×Dic26—22no—
40C2×Dic26—41no—
41C2×Dic26—41no—
42C2×Dic26—41no—
43C2×Dic26—41no—
44C2×Dic26—41no—
45C2×C8×C13—21no—
46C2×C8×C13—21no—
47C2×C8×C13—41no—
48C2×C8×C13—41no—
49C22⋊Dic13—44no—
50C22⋊Dic13—81no—
51C22⋊Dic13—81no—
52C4⋊Dic13—22no—
53C4⋊Dic13—41no—
54C4⋊Dic13—81no—
55C4⋊Dic13—81no—
56#6101—44no—
57Dic52—42no—
58Dic52—42no—
59C13×C16—81no—
60#2001—131no—
61#1314D1311yescharacteristic
62#1289—131no—
63C23×C13—21no—
64C23×C13—21no—
65C23×C13—41no—
66C23×C13—41no—
67C23×C13#10211yescharacteristic
68C23×C13SD3211yescharacteristic
69C23×C13Q3211yescharacteristic
70C2×C4×C13—21no—
71C2×C4×C13—21no—
72C2×C4×C13—21no—
73C2×C4×C13—41no—
74C2×C4×C13—41no—
75C2×C4×C13—41no—
76C2×C4×C13—81no—
77C2×C4×C13#9911yescharacteristic
78C2×C4×C13#10411yescharacteristic
79C2×Dic13—42no—
80C2×Dic13—42no—
81C2×Dic13—81no—
82C2×Dic13—81no—
83C2×Dic13—81no—
84C2×Dic13—81no—
85C2×Dic13—82no—
86C2×Dic13—82no—
87C2×Dic13—82no—
88Dic26—42no—
89Dic26—42no—
90Dic26—81no—
91Dic26—81no—
92C8×C13—41no—
93C8×C13—41no—
94C22×Q16—131no—
95C2×C22⋊Q8—261no—
96C2×#103—261no—
97C2×C22⋊C8C2×D1311yescharacteristic
98#380—261no—
99C22⋊C16—21no—
100#340—131no—
101C22×C13—21no—
102C22×C13—21no—
103C22×C13—21no—
104C22×C13—21no—
105C22×C13—41no—
106C22×C13—41no—
107C22×C13—41no—
108C22×C13—41no—
109C22×C13—81no—
110C22×C13#32711yescharacteristic
111C22×C13#35811yescharacteristic
112C22×C13#36011yescharacteristic
113C4×C13—21no—
114C4×C13—41no—
115C4×C13AΣL(1,𝔽16)11yescharacteristic
116C4×C13#35311yescharacteristic
117Dic13—82no—
118Dic13—82no—
119Dic13—162no—
120C22×Q8—261no—
121C23×C4D5211yescharacteristic
122C2×Q16—521no—
123C2×Q16—522no—
124C22×C8C4×D1311yescharacteristic
125C22×C8C22⋊D1311yescharacteristic
126C22⋊Q8—522no—
127C22⋊Q8—522no—
128C2×C4⋊C4—261no—
129C2×C4⋊C4—521no—
130C2×C4⋊C4—521no—
131C2×C22⋊C4—521no—
132C2×C22⋊C4—521no—
133C2×C16—41no—
134#103—522no—
135C22⋊C8—41no—
136#95—262no—
137C2×C13—21no—
138C2×C13—21no—
139C2×C13—41no—
140C2×C13—41no—
141C2×C13#134011yescharacteristic
142C2×C13#134311yescharacteristic
143C2×C13#134811yescharacteristic
144C24D10411yescharacteristic
145C2×Q8—262no—
146C2×Q8—521no—
147C2×Q8—521no—
148C2×Q8—521no—
149C2×Q8—521no—
150C2×Q8—521no—
151C22×C4—21no—
152C22×C4—21no—
153C22×C4—41no—
154C22×C4—41no—
155C22×C4—521no—
156C22×C4—521no—
157C22×C4—522no—
158C22×C4#609511yescharacteristic
159C22×C4#610311yescharacteristic
160Q16—522no—
161Q16—522no—
162C2×C8—21no—
163C2×C8—21no—
164C2×C8—41no—
165C2×C8—41no—
166C4⋊C4—262no—
167C4⋊C4—521no—
168C4⋊C4—524no—
169C4⋊C4—1041no—
170C4⋊C4—1041no—
171C22⋊C4—524no—
172C22⋊C4—1041no—
173C22⋊C4—1041no—
174C16—81no—
175C13#707811yescharacteristic, complemented, Sylow
176C23—21no—
177C23—21no—
178C23—41no—
179C23—41no—
180C23#8804011yescharacteristic
181C23Dic10411yescharacteristic
182C23#8806111yescharacteristic
183Q8—522no—
184Q8—522no—
185Q8—1041no—
186Q8—1041no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—81no—
194C2×C4—522no—
195C2×C4—522no—
196C2×C4—1041no—
197C2×C4—1041no—
198C2×C4—1041no—
199C2×C4—1041no—
200C2×C4—1042no—
201C2×C4—1042no—
202C2×C4—1042no—
203C2×C4#8804611yescharacteristic
204C2×C4#8806511yescharacteristic
205C8—41no—
206C8—41no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—41no—
212C22—41no—
213C22—41no—
214C22—41no—
215C22—81no—
216C22#1171806211yescharacteristic
217C22#1171809511yescharacteristic
218C22#1171811011yescharacteristic
219C4—21no—
220C4—41no—
221C4—1042no—
222C4—1042no—
223C4—2082no—
224C4#1171806611yescharacteristic
225C4#1171806711yescharacteristic
226C2—21no—
227C2—21no—
228C2—41no—
229C2—41no—
230C2#1311282511yescharacteristic
231C2#1311283411yescharacteristic
232C2#1311284911yescharacteristic
subgroupG/H
centerC22#11718062
commutatorC22×C8×C13C2×C4
FrattiniC2×C22⋊C8C2×D13
FittingC13×#1314C2
socleC22×C13#327
prime radicalC24×C13D8
cosocleC2×C13×C22⋊C8C22
hypercenter#1314D13
hypocenterC13#7078
LCSG ▷ C22×C8×C13 ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C8 ◁ #1314

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
5. C22×Dic52C4semidirect
10. #11718143C4semidirect
175. C13#7078semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#131158462
#131127042
C13×#13142
#707813